Mixed mode (I and II) crack tip fields in bulk metallic glasses

Stationary crack tip fields in bulk metallic glasses under mixed mode (I and II) loading are studied through detailed finite element simulations assuming plane strain, small scale yielding conditions. The influence of internal friction or pressure sensitivity on the plastic zones. notch deformation, stress and plastic strain fields is examined for different mode mixities. Under mixed mode loading, the notch deforms into a shape such that one part of its surface sharpens while the other part blunts. Increase in mode If component of loading dramatically enhances the normalized plastic zone size, lowers the stresses but significantly elevates the plastic strain levels near the notch tip. Higher internal friction reduces the peak tangential stress but increases the plastic strain and stretching near the blunted part of the notch. The simulated shear bands are straight and extend over a long distance ahead of the notch tip under mode II dominant loading. The possible variations of fracture toughness with mode mixity corresponding to failure by brittle micro-cracking and ductile shear banding are predicted employing two simple fracture criteria. The salient results from finite element simulations are validated by comparison with those from mixed mode (I and II) fracture experiments on a Zr-based bulk metallic glass.

A finite element analysis of quasistatic crack growth in a pressure sensitive constrained ductile layer

Polymeric adhesive layers are employed for bonding two components in a wide variety of technological applications, It has been observed that, unlike in metals, the yield behavior of polymers is affected by the state of hydrostatic stress. In this work, the effect of pressure sensitivity of yielding and layer thickness on quasistatic interfacial crack growth in a ductile adhesive layer is investigated. To this end, finite deformation, finite element analyses of a cracked sandwiched layer are carried out under plane strain, small-scale yielding conditions for a wide range of mode mixities. The Drucker-Prager constitutive equations are employed to represent the behavior of the layer. Crack propagation is simulated through a cohesive zone model, in which the interface is assumed to follow a prescribed traction-separation law. The results show that for a given mode mixity, the steady state Fracture toughness [K](ss) is enhanced as the degree of pressure sensitivity increases. Further, for a given level of pressure sensitivity, [K](ss) increases steeply as mode Il loading is approached. (C) 2000 Elsevier Science Ltd. All rights reserved.

On the mechanism and the length scales involved in the ductile fracture of a bulk metallic glass

Some bulk metallic glasses (BMGs) exhibit high crack initiation toughness due to shear band mediated plastic flow at the crack tip and yet do not display additional resistance to crack growth due to the lack of a microstructure. Thus, at crack initiation, the fracture behavior of BMGs transits from that of ductile alloys to that of brittle ceramics. In this paper, we attempt to understand the physics behind the characteristic length from the notch root at which this transition occurs, through testing of four-point bend specimens made of a nominally ductile Zr-based BMG in three different structural states. In the as-cast state, both symmetric (mode I) and asymmetric (mixed mode) bend specimens are tested. The process of shear band mediated plastic flow followed by crack initiation at the notch root was monitored through in situ imaging. Results show that stable crack growth occurs inside a dominant shear band through a distance of, similar to 60 mu m, irrespective of the structural state and mode mixity, before attaining criticality. Detailed finite element simulations show that this length corresponds to the distance from the notch root over which a positive hydrostatic stress gradient prevails. The mean ridge heights on fractured surfaces are found to correlate with the toughness of the BMG. The Argon and Salama model, which is based on the meniscus instability phenomenon at the notch root, is modified to explain the experimentally observed physics of fracture in ductile BMGs. (C) 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Effects of Microstructure and Loading on Fracture of Sn-3.8Ag-0.7Cu Joints on Cu Substrates with ENIG Surface Finish

When dropped, electronic packages often undergo failure by propagation of an interfacial crack in solder joints under a combination of tensile and shear loading. Hence, it is crucial to understand and predict the fracture behavior of solder joints under mixed-mode high-rate loading conditions. In this work, the effects of the loading conditions (strain rate and loading angle) and microstructure interfacial intermetallic compound (IMC) morphology and solder yield strength] on the mixed-mode fracture toughness of Sn-3.8 wt.%Ag-0.7 wt.%Cu solder joints sandwiched between two Cu substrates with electroless nickel immersion gold (ENIG) metallization have been studied, and compared with the fracture behavior of joints attached to bare Cu. Irrespective of the surface finish, the fracture toughness of the solder joints decreased monotonically with strain rate and mode-mixity, both resulting in increased fracture proportion through the interfacial IMC layer. Furthermore, the proportion of crack propagation through the interfacial IMC layer increased with increase in the thickness and the roughness of the interfacial IMC layer and the yield strength of the solder, resulting in a decrease in the fracture toughness of the joint. However, under most conditions, solder joints with ENIG finish showed higher resistance to fracture than joints attached directly to Cu substrates without ENIG metallization. Based on the experimental observations, a fracture mechanism map is constructed correlating the yield strength of the solder, the morphology and thickness of the interfacial IMC, and the fracture mechanisms as well as the fracture toughness values for different solder joints under mode I loading.

A general methodology for calculating mixed mode stress intensity factors and fracture toughness of solder joints with interfacial cracks

Solder joints in electronic packages undergo thermo-mechanical cycling, resulting in nucleation of micro-cracks, especially at the solder/bond-pad interface, which may lead to fracture of the joints. The fracture toughness of a solder joint depends on material properties, process conditions and service history, as well as strain rate and mode-mixity. This paper reports on a methodology for determining the mixed-mode fracture toughness of solder joints with an interfacial starter-crack, using a modified compact mixed mode (CMM) specimen containing an adhesive joint. Expressions for stress intensity factor (K) and strain energy release rate (G) are developed, using a combination of experiments and finite element (FE) analysis. In this methodology, crack length dependent geometry factors to convert for the modified CMM sample are first obtained via the crack-tip opening displacement (CTOD)-based linear extrapolation method to calculate the under far-field mode I and II conditions (f(1a) and f(2a)), (ii) generation of a master-plot to determine a(c), and (iii) computation of K and G to analyze the fracture behavior of joints. The developed methodology was verified using J-integral calculations, and was also used to calculate experimental fracture toughness values of a few lead-free solder-Cu joints. (C) 2014 Elsevier Ltd. All rights reserved.

Mixed Mode Analysis of Obliquely Oriented Edge Cracked Semicircular Disk Under Compression

A new mixed-mode compression fracture specimen, obliquely oriented edge cracked semicircular disk (OECSD) is analyzed by extending pure opening mode configuration of edge cracked semicircular disk (ECSD) under Hertzian compression. Photoelastic experiments are conducted on two different specimens of OECSD of same size and different crack lengths and inclinations. Finite element method (FEM) is used to solve a number of cases of the problem varying crack length and crack inclination. FE results show a good match with experiments. Inclination of edge crack in OECSD can be so made as to obtain any mode-mixity ratio between zero and one and beyond for any crack length. The new specimen can be used for fracture testing under compression more conveniently than the existing ones in several ways.

Crack extension and kinking in laminates and bicrystals

Singular fields at the tip of an interface crack in anisotropic solids are reviewed with emphasis on establishing a framework to quantify fracture resistance under mixed mode conditions. The concepts of mode mixity and surface toughness are unified by using generalized interface traction components. The similarity between the anisotropic theory and existing isotropic theory is shown. Explicit formulae are given for misoriented orthotropic bimaterials with potential applications envisioned including composite laminates and semiconductor crystals. Competition between crack extension along the interface and kinking into the substrate is investigated using a boundary layer formulation. Several case studies reveal the role of anisotropy. An explicit complex variable representation for orthotropic materials and a solution to a dislocation interacting with a crack are presented in two self-contained Appendices.

First principles based predictions of the toughness of a metal/oxide interface

We describe a first-principles-based strategy to predict the macroscopic toughness of a gamma-Ni(Al)/alpha-Al2O3 interface. Density functional theory calculations are used to ascertain energy changes upon displacing the two materials adjacent to the interface, with relaxation conducted over all atoms located within adjoining rows. Traction/displacernent curves are obtained from derivatives of the energy. Calculations are performed in mode I (opening), mode II (shear) and at a phase angle of 45 degrees. The shear calculations are conducted for displacements along < 110 > and < 112 > of the Ni lattice. A generalized interface potential function is used to characterize the results. Initial fitting to both the shear and normal stress results is required to calibrate the unknowns. Thereafter, consistency is established by using the potential to predict other traction quantities. The potential is incorporated as a traction/displacement function within a cohesive zone model and used to predict the steady-state toughness of the interface. For this purpose, the plasticity of the Ni alloy must be known, including the plasticity length scale. Measurements obtained for a gamma-Ni superalloy are used and the toughness predicted over the full range of mode mixity. Additional results for a range of alloys are used to demonstrate the influences of yield strength and length scale.

First principles based predictions of the toughness of a metal/oxide interface

We describe a first-principles-based strategy to predict the macroscopic toughness of a gamma-Ni(Al)/alpha-Al2O3 interface. Density functional theory calculations are used to ascertain energy changes upon displacing the two materials adjacent to the interface, with relaxation conducted over all atoms located within adjoining rows. Traction/displacernent curves are obtained from derivatives of the energy. Calculations are performed in mode I (opening), mode II (shear) and at a phase angle of 45 degrees. The shear calculations are conducted for displacements along < 110 > and < 112 > of the Ni lattice. A generalized interface potential function is used to characterize the results. Initial fitting to both the shear and normal stress results is required to calibrate the unknowns. Thereafter, consistency is established by using the potential to predict other traction quantities. The potential is incorporated as a traction/displacement function within a cohesive zone model and used to predict the steady-state toughness of the interface. For this purpose, the plasticity of the Ni alloy must be known, including the plasticity length scale. Measurements obtained for a gamma-Ni superalloy are used and the toughness predicted over the full range of mode mixity. Additional results for a range of alloys are used to demonstrate the influences of yield strength and length scale.

La densité et la marche : perceptions et pratiques de parents de jeunes enfants dans deux quartiers montréalais

La densification de la ville est l’un des principaux objectifs de l’action publique pour bâtir des milieux de vie de qualité. Mais la densité est un concept polysémique et relatif : on constate un écart entre la densité telle qu’elle est préconisée en aménagement et celle vécue par les populations. Parallèlement, on observe l’exode des jeunes familles montréalaises vers les territoires périurbains de faible densité. Enfin, la littérature souligne une relation positive entre densité, mixité et pratique de la marche. Cette recherche explore les perceptions des parents de jeunes enfants à l’égard de leur environnement bâti, en particulier de sa densité, et en identifie les facteurs qui influencent positivement leur pratique de la marche. Après avoir caractérisé les formes urbaines de deux quartiers montréalais aux densités différentes, nous avons interrogé des parents de jeunes enfants sur leur expérience lors de 16 entrevues semi-dirigées et d’un groupe de discussion. Puis nous avons étudié la relation entre les variables personnelles des participants, leurs perceptions de la densité et leurs pratiques de la marche. Nos résultats mettent en évidence la quête d’un équilibre entre les avantages et inconvénients de la densité, dont les principales variables sont les formes urbaines, les services de proximité et la présence d’animation, la végétation étant un paramètre incontournable pour tous les parents. Caractéristiques clés d’une ville intense, ces paramètres corroborent la littérature existante à ce sujet, en mettant en évidence leur importance dans la création de milieux de vie plus denses pour les jeunes familles et leur influence positive sur la marche.

Interfacial fracture of dentin adhesively bonded to quartz-fiber reinforced composite

The paper presents the results of an experimental study of interfacial failure in a multilayered structure consisting of a dentin/resin cement/quartz-fiber reinforced composite (FRC). Slices of dentin close to the pulp chamber were sandwiched by two half-circle discs made of a quartz-fiber reinforced composite, bonded with bonding agent (All-bond 2, BISCO, Schaumburg) and resin cement (Duo-link. BISCO, Schaumburg) to make Brazil-nut sandwich specimens for interfacial toughness testing. Interfacial fracture toughness (strain energy release rate, G) was measured as a function of mode mixity by changing loading angles from 0 degrees to 15 degrees. The interfacial fracture surfaces were then examined using Scanning Electron Microscopy (SEM) and Energy Dispersive X-ray Spectroscopy (EDX) to determine the failure modes when loading angles changed. A computational model was also developed to calculate the driving forces, stress intensity factors and mode mixities. Interfacial toughness increased from approximate to 1.5 to 3.2 J/m(2) when the loading angle increases from approximate to 0, 0 to 15 degrees. The hybridized dentin/cement interface appeared to be tougher than the resin cement/quartz-fiber reinforced epoxy. The Brazil-nut sandwich specimen was a suitable method to investigate the mechanical integrity of dentin/cement/FRC interfaces. (C) 2011 Elsevier B.V. All rights reserved.

Computational modeling of laser-induced delamination testing of thin films

Thin film adhesion often determines microelectronic device reliability and it is therefore essential to have experimental techniques that accurately and efficiently characterize it. Laser-induced delamination is a novel technique that uses laser-generated stress waves to load thin films at high strain rates and extract the fracture toughness of the film/substrate interface. The effectiveness of the technique in measuring the interface properties of metallic films has been documented in previous studies. The objective of the current effort is to model the effect of residual stresses on the dynamic delamination of thin films. Residual stresses can be high enough to affect the crack advance and the mode mixity of the delimitation event, and must therefore be adequately modeled to make accurate and repeatable predictions of fracture toughness. The equivalent axial force and bending moment generated by the residual stresses are included in a dynamic, nonlinear finite element model of the delaminating film, and the impact of residual stresses on the final extent of the interfacial crack, the relative contribution of shear failure, and the deformed shape of the delaminated film is studied in detail. Another objective of the study is to develop techniques to address issues related to the testing of polymeric films. These type of films adhere well to silicon and the resulting crack advance is often much smaller than for metallic films, making the extraction of the interface fracture toughness more difficult. The use of an inertial layer which enhances the amount of kinetic energy trapped in the film and thus the crack advance is examined. It is determined that the inertial layer does improve the crack advance, although in a relatively limited fashion. The high interface toughness of polymer films often causes the film to fail cohesively when the crack front leaves the weakly bonded region and enters the strong interface. The use of a tapered pre-crack region that provides a more gradual transition to the strong interface is examined. The tapered triangular pre-crack geometry is found to be effective in reducing the stresses induced thereby making it an attractive option. We conclude by studying the impact of modifying the pre-crack geometry to enable the testing of multiple polymer films.